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Muon Collider Collaboration Meeting Berkeley, Oct 2002. Window Thermal /flow Analysis. Wing Lau & Stephanie Yang Oxford University. This discussion is split into two parts:
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Muon Collider Collaboration MeetingBerkeley, Oct 2002 Window Thermal /flow Analysis Wing Lau & Stephanie Yang Oxford University
This discussion is split into two parts: In the first part, we continue with our discussion on the force flow design, the 3-D results and our understanding on how to make the flow more effective in the case of an active cooling system; In the second part, we look at the convective window and how its cooling performance reacts to different heat sources.
The progress so far We have examined the flow characteristic of Liquid Hydrogen inside the Absorber window at various flow speeds using a series of 2-D FE models. Ideally, such complex analysis warrants the need to have a 3-D grid model to do the job. But 3-D model is complicated to build and takes up enormous computing power to analyse. When the final geometry and arrangement of the nozzles and their manifold are still being iterated on the design board, it would be pointless to spend all the effort in building such complex model, only to be thrown away every time the design is changed. We chose instead to set up a series of 2-D models which are easy to build and run and which provide us sufficient insight to what would be the best nozzle arrangements and flow speeds etc for the purpose of what we are trying to achieve. That exercise is more or less completed. The 2-D models suggested that at very low speed – below 1m/s, the LH2 inside the Absorber is not sufficient to remove all the heat that are deposited on it by the Muon Beam. Depending on the final confirmation of the Beam’s effective diameter, a higher flow rate, exceeding well beyond 2 m/s may be required if the Absorber window is to be kept within a reasonable temperature level, and that the LH2 is prevented from reaching the boiling temperature. But this is in direct conflict with the Cryogenic design requirement which asks that the flow speed to be kept to around 0.56 m/s so that the pressure loss can be kept to an acceptable level for the cryogenic pumps etc
However, what we know from the 2-D analyses is that we do need to establish a “flow path” which covers the underside of the upper Window surface to prevent the window from building up any local hot spot. That flow path is achieved by placing the nozzles at around 20 degree to the horizontal and at a flow speed of around 4 - 5 m/s. • There are several areas in the 2-D model which could lead to unrealistic results. These are:- • Flow being artificially kept to a single plane. In reality, some of the flow will deviate from the prescribed 2-D plane and “branch” out to the third dimensional planes The lack of this in a 2-D model will make the results too optimistic; • The addition of a second set of nozzles, covering the lower surface of the Window, has a marked effect on the cooling performance. However, these additional nozzles are strictly speaking not in the right place. They share the same plane as the other nozzles. In reality they should be off-set circumferentially from each other. • The lack of interactive between flow speed and heat removal capacity in a 2-D model gives insufficient information on what is the acceptable speed for the purpose of cooling, i.e. is it necessary for a flow path to be established to cool the Window to the required temperature level? Only a 3-D model can provide the necessary information.
2-D model with one nozzle set 2-D model with 2 nozzle sets Effective beam diameter assumed to be 45mm
So, what is a 3-D model look like and what does it tell us about the flow pattern?
Steady state 2-D flow pattern Steady state 3-D flow pattern
Conclusion on the force flow Window design A comment was made at the last MuCool meeting questioning the suitability of using an FE software, which was largely developed for structural analysis, for a highly complex fluid flow problem. Our initial reaction was that Algor’s fluid dynamic model is fit for the purpose. We had carried out numerous test runs and found that the results compare well with known bench mark results. However, we acknowledge the fact that Algor’s 3-D model built is difficult to set up and time consuming to run. Furthermore, it does not have the fluid / thermal interactive capability that is required for our type of analysis. For that reason, we have installed the CFX software which is widely recognised as the ultimate tool for non-linear fluid / thermal interactive analysis. Initial results show that Algor’s 2-D results are very close to the CFD’s 3-D results on the same 2-D plane. The characteristics of the flow, which is largely lamina because of the pressure head restriction, is such that fluids are coming out of the inlet nozzle and flow straight towards the outlet nozzle, leaving very little to “stray” into the third dimension, as shown in the above 3-D plots. For this reason, we will still use Algor to do most of the exploratory runs because of its low CPU requirements. However, when it comes to the fluid / thermal interactive analysis, the CFX will be our ultimate tool to use, and we shall use it well in the next coming months
What’s next? We believe we have built up a credible approach in analysing the complex 3-D flow pattern of LH2 and to examine its thermal removal capacity. Our next priority is to agree with the Cryogenic design group on the maximum number of nozzles, their diameter and the acceptable flow speeds etc so that we can see if the imposed restrictions can produced the kind of flow that meets the cooling requirement. Once that is done, our ultimate goal is to produce a set of graphs showing nozzle geometries, quantity and flow speeds against the cooling power of the Absorber. In addition, we would like to examine the scenario when local boiling of liquid occurs and the build up of pressures inside the window. This will be useful in looking at the safety issues of this Window design
The Convective Heat analysis • An 3-D grid was built on a 30cm diameter torispherical window geometry. The reason for choosing this geometry as a reference model is that we would wish to compare our analytical results with the experimental data from KEK who has built and tested the window performance, albeit with different coolant; • Consequently, the geometry of the heat source assumes that of the dummy coil heater from KEK’s test model; • We have studied the convective heat flow with 4 difference heat input. These are: • 80 W; • 60 W; • 40 W; • 450 W • The first three are the sensitivity study, aiming to find out how sensitive the LH2 reacts to the slight change in the heat source. The last one is aim at the MuCool experiment, albeit the volume of the absorber in the lab G experiment will not be the same
Boundary conditions and reservations: The Window is assumed to be cooled by a constant supply of either LHe at 4K or gas LHe at 17K to prevent the LHe from solidifying. In our analysis, we have assumed that the window wall is at a constant temperature of 17K for heat source of 80W and less, and at 4K for 450W; For the 450W heat input case, we have assumed that the LH2 are all at an even temperature 17K when cooling starts. In practice, the LH2 is being kept to above freezing point by a coil heater. This may have already generated a convection current flow inside the window when cooling starts. We have not included that in our current analysis, but will be added in at a later stage once we know the detail arrangement of the heating coils;
Liquid Hydrogen Heating Coil The 3-D Grid for the convective heat flow analysis
Conclusion on the Convective Window design The study shows that when the heat source is low, there is very little change in fluid temperature. For a heat load of 80W, fluid temperature rose by a mere 2K; We believe the heat source from MICE is below this value, and we can conclude that the design is suitable for the MICE experiment; For the MuCool experiment however, the heat input is in the region of 450W. The analysis shows that the convective window design may not have sufficient cooling power to remove all the heat whilst keeping the LH2 below its boiling temperature even using LHe as the secondary cooling to keep the window wall at 4K at all time; The results so far point to the fact that for the MuCool experiment, the Convective Window may not be a suitable candidate for the job; We invite interesting parties to examine the results of our analyses in details so that any recommendation to discard the Convective window design for the MuCool experiment receives the endorsement of the project collaborators
